What are some real-life applications of integration and differentiation?

It’s an age-old question in math class: When am I ever going to use this in real life? Unlike basic arithmetic or finances, calculus may not have obvious applications to everyday life. However, people benefit from the applications of calculus every day, from computer algorithms to modeling the spread of disease. While you may not sit down and solve a tricky differential equation on a daily basis, calculus is still all around you.

Weather Models

Weather is more accurately predicted than ever before. Part of the improvement is thanks to technology, such as computer modeling that uses calculus and is able to more meticulously predict upcoming weather. These computer programs also use types of algorithms to help assign possible weather outcomes in a region. Much like in the computer algorithms, weather forecasts are determined by considering many variables, such as wind speed, moisture level and temperature. Though computers do the heavy lifting of sifting through massive amounts of data, the basics of meteorology are grounded in differential equations, helping meteorologists determine how changes in the temperatures and pressures in the atmosphere may indicate changes in the weather.

Improving Public Health

The field of epidemiology — the study of the spread of infectious disease — relies heavily on calculus. Such calculations have to take three main factors into account: those people who are susceptible to a disease, those who are infected with the disease and those who have already recovered from it. With these three variables, calculus can be used to determine how far and fast a disease is spreading, where it may have originated from and how to best treat it. Calculus is especially important in cases such as this because rates of infection and recovery change over time, so the equations must be dynamic enough to respond to the new models evolving every day.


Calculus is used to improve the architecture not only of buildings but also of important infrastructures such as bridges. Bridges are complex constructions because they have to be able to support varying amounts of weight across large spaces. When designing a bridge, one must take into account factors including weight, environmental factors and distance. Because of this, maths such as differential calculus and integral calculus are often used to create the most robust design. The use of calculus is also creating a change in the way other architecture projects are designed, pushing the frontier of what sorts of shapes can be used to create the most beautiful buildings. For example, though many buildings have arches with perfect symmetry, calculus can be used to create archways that are not symmetric along with other odd shapes that are still able to be structurally sound.

Solving complex Electrical resistor problems using simple methods from Matrices, or the time when I saw how to apply Integrations in Thermodynamics(I won’t get into it), or to understand how markets and economics work based on some function and you can predict the future which doesn’t sound true, all of this sounded pretty confusing in the start.

But I bet you’ll gain a much broader sense of understanding if you keep doing what you are doing because you are trying to find out why, which as many eminent personalities have stated that, it is the right way to life.

  1. Fan is running because of electricity  which needed a way lot more Calculus than you imagined,
  2. Air conditioners work on the heat flow principles which involve Calculus,
  3. Your bike’s engine is working on the principles of conversion of energy from chemical to heat to mechanical which needed a way lot more Calculus than you imagined,
  4. You travel in planes which are created on the principles of Aerodynamics whose key concept would again be Calculus,
  5. Computer, iPhone, Tablet, bulbs might have had some Calculus induced in them before they are in front of you.
  6. Okay, this proves it. Every machine made thing/item required a machine. But Calculus is used to design those machines. So basically, it is goddamn EVERYWHERE!
  7. What about the fields of Chemistry, Economics, Biology, Geology, or any other ‘logy’ in which Calculus is used?